CPi-PS (Common-Path interferometry with Phase-Shifting)

All selected domains feature publicly accessible datasets:
Seismic: USGS Earthquake Catalog (https://earthquake.usgs.gov/), IRIS Seismic Data Portal
Weather: NOAA Global Historical Climatology Network (https://www.ncei.noaa.gov/products/land-based-station/global-historical-climatology-network-daily)
Financial: Alpha Vantage API, Yahoo Finance (yfinance library), FNSPID dataset
Cryptocurrency: CryptoDataDownload, exchange APIs (Binance, Coinbase)

This research tests whether physics-informed principles derived from Sagnac common-path interferometry can be effectively transposed to time series noise filtering. The hypothesis posits that analyzing phase coherence in the frequency domain will outperform traditional amplitude-based denoising methods (Extended Kalman Filter, Wavelet Transform, Exponential Smoothing). The core premise is that genuine signal components exhibit consistent phase relationships across frequency bands, while noise components display random phase distributions—enabling more precise discrimination between signal and noise.

Data Description
Dataset Structure: This dataset contains raw time series data and filtered outputs from a comprehensive validation study of the CPi-PS (Common-Path Interferometry with Phase-Shifting) framework. The study compares four denoising methods across 16 real-world time series spanning five application domains, yielding 64 experimental conditions.

Data Sources:

Commodity data: Daily prices for Copper, Crude Oil, Gasoline, Gold, Natural Gas, and Silver (6 variables, 18,449 daily observations)
Weather data: Daily temperature and precipitation records (2 variables, 2,189 daily observations)
Seismic data: Earthquake magnitude measurements (1 variable, 9,415 event-based observations)
Cryptocurrency data: Bitcoin and Ethereum daily closing prices (2 variables, 4,435 daily observations)
Financial index data: Dow Jones, S&P 500, JPM, MSFT, and TSLA closing prices (5 variables, 7,619 trading day observations)

Data Interpretation Guidelines
The results validate that transposing interferometric phase coherence principles to frequency domain analysis effectively discriminates signal from noise. The method is particularly effective for time series with underlying deterministic structure (financial data) and less effective for intrinsically stochastic phenomena (seismic events, precipitation). Users should select methods based on domain: CPi-PS is recommended for most applications; WT serves as a strong alternative; EKF suits known linear state-space models; ExpSmooth is not recommended for preprocessing due to phase distortion.

Data Usage: Raw data can benchmark new denoising algorithms; filtered outputs serve as preprocessed ML inputs; metrics provide baseline comparisons for method development.